If a disbeliever doesn't forgive me in this life for wronging him, is it possible that Allah can punish me in this life instead of punishing me in the hereafter?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

We previously answered your question in Fatwa number 281386, saying that it is prohibited for a Muslim to wrong any person, be it a Muslim or a non-Muslim. If a Muslim commits any act of injustice against a non-Muslim, it is incumbent on him to seek the forgiveness and pardon of the wronged person and were he to die prior to that, the wronged person will be given the chance to retaliate on the Day of Judgment.

As for your question whether Allaah will punish you for your injustice in this worldly life instead of the Hereafter, this is in the hands of Allaah, The Exalted. If He wills, He will compensate the wronged non-Muslim for your injustice in this worldly life or in the Hereafter by lessening his punishment, and He may also punish you for your injustice in the Hereafter, if He so wills. The point is that Allaah does not allow any wronged person's right to retaliation to be lost, even if it is a non-Muslim.

The Prophet, sallallaahu ‘alayhi wa sallam, said in a Qudsi (Sacred) Hadeeth: "Allaah will say on the Day of Judgment, 'I am the King. I am the Judge. It is not for any one of the people of the Fire to enter the Fire when someone from the people of Paradise has a right that belongs to him until I avenge him, and it is not for any one of the people of Paradise to enter Paradise when he has a right that belongs to someone from the people of the Fire until I avenge him, even a slap." People asked, "How will that be, when we will be resurrected before Allaah naked, uncircumcised and having nothing with us?" He, sallallaahu ‘alayhi wa sallam, said: "With good and bad deeds." [Ahmad - Al-Albaani graded it Hasan (good)]

The most important thing for you to do is to be diligent in achieving sincere repentance from such injustice.

Allaah Knows best.